The Likelihood Ratio Framework
Paternity testing frames identity as a hypothesis test. The prosecution hypothesis H1 states the alleged father is the true biological father; the defense hypothesis H2 states a random unrelated man from the population is the father. At each STR locus, the likelihood ratio quantifies how much more probable the observed child-mother-alleged father genotype trio is under H1 versus H2.
Combining Evidence Across Loci
Because STR loci on different chromosomes segregate independently, per-locus paternity indices multiply to form the Combined Paternity Index. Sixteen loci with modest individual PIs of 2-3 each produce a CPI in the millions, translating to probabilities of paternity exceeding 99.9999%. This exponential accumulation of evidence is the statistical engine of kinship testing.
Mutation Considerations
STR loci mutate at measurable rates, typically 0.1-0.6% per generation. A true father-child pair may show a one-repeat mismatch at a single locus due to germline mutation. Modern laboratories never exclude on a single mismatch; instead they calculate a mutation-adjusted PI using the known mutation rate, which reduces but does not eliminate the evidence at that locus.
Legal Standards and Reporting
Courts worldwide have adopted the PI/W framework with varying thresholds. The AABB requires testing at a minimum of 15 loci and reporting both the CPI and the posterior probability. The ISFG recommends transparent reporting of assumptions including population databases used, mutation models applied, and prior probability chosen.